We prove that Sharma-Mittal entropy is a subadditive and supermodular function on the lattice of all $n$-dimensional probability distributions, ordered according to the partial order relation defined by majorization among vectors. Our result unifies and extends analogous results presented in the literature for the Shannon entropy, the Tsallis entropy, and the Rényi entropy.

翻译：我们证明，在所有$n$维概率分布构成的格上，夏尔马-米塔尔熵是关于向量主序偏序关系的次可加和超模函数。该结果统一并推广了文献中关于香农熵、Tsallis熵和Rényi熵的类似结论。